A339549 a(n) is the product of the binary weights (A000120) of the divisors of n.

1, 1, 2, 1, 2, 4, 3, 1, 4, 4, 3, 8, 3, 9, 16, 1, 2, 16, 3, 8, 18, 9, 4, 16, 6, 9, 16, 27, 4, 256, 5, 1, 12, 4, 18, 64, 3, 9, 24, 16, 3, 324, 4, 27, 128, 16, 5, 32, 9, 36, 16, 27, 4, 256, 30, 81, 24, 16, 5, 4096, 5, 25, 216, 1, 12, 144, 3, 8, 24, 324, 4, 256, 3

Offset

1,3

Comments

Analogous to A093653 with product instead of sum.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = Product_{d|n} A000120(d).

a(n) = 1 if and only if n is a power of 2 (A000079).

Example

a(6) = 4 since the divisors of 6 are {1, 2, 3, 6}, and in binary representation {1, 10, 11, 110}. The number of 1's are {1, 1, 2, 2} and their product is 1*1*2*2 = 4.

Mathematica

a[n_] := Times @@ (DigitCount[#, 2, 1] & /@ Divisors[n]); Array[a, 100]

Prog

(PARI) a(n) = vecprod(apply(hammingweight, divisors(n))); \\ Michel Marcus, Dec 08 2020

Crossrefs

Cf. A000079, A000120, A093653.

Sequence in context: A120855 A193737 A160001 * A179750 A091173 A101897

Adjacent sequences: A339546 A339547 A339548 * A339550 A339551 A339552

Keyword

nonn,base

Author

Amiram Eldar, Dec 08 2020

Status

approved